Number Of Additional Terms Research Articles

Greens tensor of a weakly anisotropic cubic crystal: Efficiency of point defect absorption by spherical pore

Using the Lifshitz-Rozentsveig method, an improved expression for the Green tensor in the case of a weakly anisotropic cubic crystal has been derived. It contains a number of additional terms disregard previously. An expression for the energy of elastic interaction of a point defect with a gas-filled pore, which differs from its analogue (commonly used referring to Eshelby) by an additional factor in the radial part, has been derived. In the case of weak interaction (in comparison with thermal energy), a correction to the efficiency of point defect absorption by a gas-filled pore is obtained, which appears quadratic in the anisotropy parameter and negative. As a result, the pore exhibits preference for absorption of vacancies in comparison with absorption of interstitials.

Classical tests in brane gravity

The vacuum solutions in brane gravity differ from those in 4D by a number of additional terms and reduce to the familiar Schwarzschild metric at small distances. We study the possible roles that such terms may play in the precession of planetary orbits, bending of light, radar retardation and the anomaly in mean motion of test bodies. Using the available data from solar system experiments, we determine the range of the free parameters associated with the linear term in the metric. The best results come from the anomalies in the mean motion of planets. Such studies should shed some light on the origin of dark energy via the solar system tests.

A Perturbative Approach for the Analysis of Electromagnetic Coupling Among Circular Corrugated Horns

A simple and efficient perturbative approach to analyze the electromagnetic coupling among circular horns is proposed in this paper. The method is based on an analysis tool which combines two different techniques: a mode matching (MM) technique for the propagation inside the horn and a method of moments (MoM) technique for the radiation of the horn taking into account the external part of all the horns of the cluster. The resulting linear system is solved via a very simple iterative procedure in which one can easily control the number of additive terms until the convergence is reached. The method can analyze arbitrarily large horn clusters with moderate computer resources. One of the main benefits of the new procedure is that one can exploit programs developed to analyze stand-alone horns also to evaluate the electromagnetic coupling

Optimization of some factors affecting the performance of query expansion

This paper examines the factors affecting the performance of global query expansion based on term co-occurrence data and suggests a way to maximize the retrieval effectiveness. Major parameters to be optimized through experiments are term similarity measure and the weighting scheme of additional terms. The evaluation of four similarity measures tested in query expansion reveal that mutual information and Yule's Y, which emphasize low frequency terms, achieve better performance than cosine and Jaccard coefficients that have the reverse tendency. In the evaluation of three weighting schemes, similarity weight performs well only with short queries, whereas fixed weights of approximately 0.5 and similarity rank weights were effective with queries of any length. Furthermore, the optimal similarity rank weight achieving the best overall performance seems to be the least affected by test collections and the number of additional terms. For the efficiency of retrieval, the number of additional terms needs not exceed 70 in our test collections, but the optimal number may vary according to the characteristics of the similarity measure employed.

Theory of compressible irrotational flows including heat conductivity and longitudinal viscosity

A new exact analytical model was derived for the irrotational flows of compressible fluids when the effects of heat conductivity and molecular viscosity are allowed. This new model satisfies conservation of mass, momentum and energy exactly. In addition, it satisfies physical irrotationality conditions. Compared to the classical small perturbation viscous-transonic (V-T) equation, the new physically dissipative potential (PDP) equation contains a number of additional terms that are highly nonlinear. The new model is derived in a general vector operator form and in a scalar canonical form. The PDP equation is able to produce shock waves of different strengths depending on the ratio of secondary and shear viscosity coefficients. The one-dimensional, steady flow version of the PDP equation was integrated using a Runge-Kutta scheme and different values of the ratio of the two viscosities. The computed shock structures are symmetric. Rankine-Hugoniot shock jumps were obtained when Stokes' hypothesis was used in the PDP equation and isentropic shock jumps were obtained when the longitudinal viscosity was negligible.

A method for deriving hydrodynamic equations for complicated systems

A general algorithm is proposed for constructing a uniformly valid asymptotic solution of the kinetic equations under conditions when the number of slowly varying macroscopic variables is greater than the number of integral invariants of the collision operator. The case of a chemically reacting gas mixture is considered, and a method for constructing the asymptotic solution for this case is described. The hydrodynamic equations for reacting and relaxing gas mixtures are described in general form and it is noted that consistent allowance for the disequilibrium of the reaction and relaxation processes leads to the appearance in the hydrodynamic equations of a number of additional terms, which describe the dependence of the rates of these processes on the spatial derivatives of the hydrodynamic variables.

On the shape of a slender axisymmetric nonstationary cavity

Very few studies have been made of three-dimensional nonstationary cavitation flows. In [1, 2], differential equations were obtained for the shape of a nonstationary cavity by means of a method of sources and sinks distributed along the axis of thin axisymmetric body and the cavity. In the integro-differential equation obtained in the present paper, allowance is made for a number of additional terms, and this makes it possible to dispense with the requirement ¦ In ɛ ¦ ≫ 1 adopted in [1, 2]. The obtained equation is valid under the weaker restriction ɛ ≪ 1. In [3], the problem of determining the cavity shape is reduced to a system of integral equations. Examples of calculation of the cavity shape in accordance with the non-stationary equations of [1–3] are unknown. In [4], an equation is obtained for the shape of a thin axisymmetric nonstationary cavity on the basis of a semiempirical approach. In the present paper, an integro-differential equation for the shape of a thin axisymmetric nonstationary cavity is obtained to order ɛ2 (ɛ is a small constant parameter which has the order of the transverse-to-longitudinal dimension ratio of the system consisting of the cavity-forming body, the cavity, and the closing body). A boundary-value problem is formulated and an analytic solution to the corresponding differential equation is obtained in the first approximation (to terms of order ɛ2 In ɛ), A number of concrete examples is considered.